Author: Physics Notebook
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A Cylinder Has A Mass ‘M’, Length ‘l’ And Radius ‘a’. Find The Ratio Of ‘l’ To ‘a’ If The Moment Of Inertia About An Axis Through The Centre And Perpendicular To The Length Is Minimum
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Ans. Here, the mass of the cylinder is M, radius is a and length is l. If be the density of material of the cylinder, then the mass of the cylinder is . or, (say) The moment of inertia of this cylinder about an axis passing through the centre and perpendicular to the length of…
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A Solid Spherical Ball Rolls On A Table, Find The Ratio Of Its Translational And Rotational Kinetic Energies And The Total Energy Of The Spherical Ball. What Fraction Of The Total Energy Is Rotational?
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Ans. Let us consider a spherical ball of radius r and mass M. If v be the linear velocity of the ball then the translational kinetic energy of the ball is .If be the angular velocity of the ball then the rotational kinetic energy of the ball is , [ To know the derivation of…
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A Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.
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Ans. When a circular disc of mass M and radius r rolls on a table, then its total kinetic energy E will be, = (Energy due to linear motion) + (energy due to rotational motion) The moment of inertia of a circular disc about an axis passing through the centre of the disc and perpendicular…
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Two Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.
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Ans. Here, two wheels each of mass M and radius R are rigidly connected by a weightless rod of length 2R. The moment of inertia of each wheel about their diameter is .[ To know the derivation of moment of inertia of a wheel about its own diameter, ( CLICK HERE ) ] By applying…
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Two Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.
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Ans. Here the two masses ‘m‘ and ‘M‘ are at a distance d apart. Let us consider, O be the centre of mass of the system of these two masses, be the distance of mass M from the centre of mass O and be the distance of m from the centre of mass O. So…
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A Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.
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Ans. Here the mass of the uniform rod M=5 lbs,length of the rod is l=2 ft.The rod is rotating about one end with frequency =1 rev./sec.The angular velocity is We know that the moment of inertia of the rod about on end is [ To know in details ( CLICK HERE ) ] The kinetic…
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Calculate The Kinetic Energy Of A Thin Rod Of Length ‘l’ And Mass ‘m’ Per Unit Length Rotating About An Axis Through The Middle Point And Perpendicular To Its Length With Angular Velocity ω.
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Ans: The length of the thin rod is l and mass density i.e., mass per unit length is m. So the total mass of the rod is .The rod is rotating with angular velocity about an axis passing through the middle point and perpendicular to the length of the rod. We know that the moment…
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Two Circular Metal Discs Have The Same Mass ‘M’ And The Same Thickness ‘t’. Disc ‘1’ Has A Uniform Density, Which Is Less Than That Of The Disc ‘2’. Which Disc Has The Larger Moment Of Inertia.
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Ans. For disc 1, mass and thickness are M and t respectively. Let, be the radius of the circular disc and be the uniform density of the disc. The volume of this disc is . So the mass of disc 1 is . For disc 2, mass and thickness are M and t respectively. Let…
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Obtain An Expression For The Moment Of Inertia Of A Solid Cone (i) About Its Axis Of Symmetry, (ii) About An Axis Passing Through The Vertex And Perpendicular To The Axis Of Symmetry
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(i) Moment of inertia of a solid cone about its axis of symmetry: Let us consider a right circular solid cone ABC of mass M and height h, as shown in the above Fig.1. If r be the radius of base of the solid cone then the total volume of this solid cone is .…
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Determine The Moment Of Inertia Of A Triangular Lamina (i) About One Of Its Sides, (ii) About An Axis Passing Through The Centre Of Gravity And Parallel To One Side, (iii) About An Axis Passing Through One Of Its Vertices And Parallel To Opposite Side.
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(i) Moment of inertia of a triangular lamina about one of its side: Let us consider a triangular lamina ABC of mass M, is rotating about one of its sides BC, where the length of the side BC is a. If be the height of this lamina, then the area of this lamina is and…